The rate of mixing of two liquids, the rate of dissolution of a solute in a liquid or, the homogenization of a dissolved solute in a liquid is based on the diffusion coefficients of the components, which are relatively invariable, and the flow field the fluid experiences. Thus, in systems where mixing is required, optimization of the mixing process requires an appropriate choice of fluid flow conditions. The most efficient mixing conditions are those where there is a high degree of turbulence, which takes the form of randomly swirling eddies that stretch out nonhomogeneous fluid elements and allow diffusion to take place over a very short distance, thereby providing homogeneity. However, in some devices, particularly those with small volumes, closely spaced walls, and/or capillary spaces, the range of fluid flow conditions achievable is severely limited by the viscosity of the fluid or by the dimensions of the system so that turbulence cannot be easily achieved.
In large containers a moving mixing bar or blade induces bulk movement of liquid, which results in mixing of the entire volume of the container. A well-known example of this physical phenomenon is seen in the bulk mixing that occurs as a result of magnetically induced movement of a stir bar at the bottom of a flask or beaker. In contrast, a small mixing bar that rotates in a capillary space formed by two surfaces spaced a small distance apart will mix only the volume that the bar sweeps out, since drag associated with liquid/wall contact prevents transport of momentum (motion) through the fluid by inertia of the liquid.
Diagnostic devices that use capillary flow to transport blood into the interior of the device for mixing with reagents and provide for analysis of a component or property of the blood are examples of small containers that require good mixing under difficult conditions. For example, good mixing is desirable in small rectangular chambers of such assay devices where blood and an aqueous or dry reagent must be quickly and efficiently mixed together. A chamber volume of 155 microliters is typical of some such assays, with dimensions of the chamber being 0.14 inch deep, 0.39 inch length, and 0.175 inch height. In this case a steel ball with a diameter of approximately 0.1 inches can be used to agitate the fluid by rapid back and forth movement under the influence of a magnetic field. The Reynolds number (which relates the ratio of inertia to viscous forces) for flow around the ball is approximately 600 under these circumstances, which indicates a regime where there are significant mixing eddies behind the ball as it moves. In this case, the ball comprises approximately 5% of the chamber volume, but even so, after multiple, passes of the ball, all of the fluid has experienced the mixing action. This is thus an example of a small volume that is still sufficiently large for traditional mixing techniques to be used. See, for example, U.S. Pat. No. 5,028,142, assigned to the assignee of the present application.
In contrast with the previous example, another more extreme assay situation that required the attention of the present inventors involved a cylindrical capillary space, flat on top and bottom, with a depth of 0.012 inch and a diameter of 0.28 inch (volume=12 microliters); dry reagent in this chamber needed to be mixed with whole blood after it flowed by capillary action into the chamber. If mixing were attempted magnetically with a steel ball having a diameter of 0.006 inch (i.e., one-half of the chamber height) and moving at the same speed as in the previous example, the mixing would be inefficient for a number of reasons (1) the ball is now only 0.015% of the chamber volume; (2) the Reynolds number, reduced to 10 because of the smaller ball and greater viscosity of the fluid, signifies a reduction in eddy mixing; and (3) the ball would be more difficult to oscillate because the magnetic force driving its motion decreases according to its mass (resulting in 4600-fold less driving force than in the previous example), whereas the friction force which opposes the motion decreases proportionally to the diameter of the ball and increases because of the more viscous fluid (resulting in only 4-fold less friction force than the previous example). Such physical constraints on forces present in small mixing systems therefore discourage mixing with magnetic or magnetically inducible materials in small spaces, such as capillary spaces.
Accordingly, a new technique for mixing in capillary spaces is desirable.